Transforming Absolute Value Graphs

The video tutorial introduces parent functions, focusing on linear and absolute value functions. It covers graphing techniques, domain and range, and transformations such as shifts and stretches. The tutorial also explains how to write equations for transformed functions based on given descriptions, emphasizing the importance of understanding function properties and transformations.

What is the slope of the parent linear function y = x?

• -1

• 2

• 1

• 0

What is the y-intercept of the parent linear function y = x?

• 2

• 1

• 0

• -1

In set notation, how is the domain of the linear function y = x represented?

• x such that x is an element of all real numbers

• y such that y is an element of all real numbers

• y such that y is greater than 0

• x such that x is greater than 0

What is the range of the linear function y = x in interval notation?

• (-∞, 0)

• (-∞, 0]

• [0, ∞)

• (-∞, ∞)

What is the absolute value of -2?

• -2

• 0

• 2

• -1

What is the range of the absolute value function y = |x| in set notation?

• x such that x is greater than or equal to 0

• x such that x is an element of all real numbers

• y such that y is an element of all real numbers

• y such that y is greater than or equal to 0

What does a vertical stretch by a factor of 2 do to the graph of y = |x|?

• Makes it narrower

• Shifts it up

• Shifts it down

• Makes it wider

If the graph of y = |x| is shifted 3 units to the right, what is the new equation?

• y = |x| - 3

• y = |x| + 3

• y = |x - 3|

• y = |x + 3|

How would you write the absolute value function that is translated 12 units up and 6 units left?

• y = |x + 6| - 12

• y = |x - 6| - 12

• y = |x + 6| + 12

• y = |x - 6| + 12

What does a negative sign in front of the absolute value function indicate?

• Reflection over the y-axis

• Vertical stretch

• Vertical shrink

• Reflection over the x-axis